If 5 -letter words'' are formed using the letters A, B, C, D, E, F, G, how many such words are possible for each of the following conditions? a. No condition is imposed.
b. No letter can be repeated in a word.
c. Each word must begin with the letter A and letters can be repeated.
d. The letter C must be at the end and letters can be repeated.
e. The second letter must be a vowel and letters can be repeated.

b

step-by-step explanation:

(a) common ratio in the given sequence is, 3

(b) push ups will do kendall do on the 20th week

step-by-step explanation:

geometric sequence is a sequence of numbers that follows a pattern were the next term is found by multiplying by a constant called the common ratio(r)

(a)

given the sequence: 6 , 18 , 54 , 162 ,

this sequence is geometric sequence where each term is 3 times the previous term.

therefore,

common ratio(r) = 3.

(b)

a formula for nth term of geometric sequence is given by;

,   where r is the common ratio between the successive terms and is the first term,

to find how many push ups will kendall do on the 20th week.

here. n = 20th term.

in the given sequence first term

then;

simplify:

therefore, push ups will do kendall do on the 20th week